Question: Simplify the following expression: $x = \dfrac{10p^2 - 190p + 900}{p - 10} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $10$ , so we can rewrite the expression: $ x =\dfrac{10(p^2 - 19p + 90)}{p - 10} $ Then we factor the remaining polynomial: $p^2 {-19}p + {90} $ ${-10} {-9} = {-19}$ ${-10} \times {-9} = {90}$ $ (p {-10}) (p {-9}) $ This gives us a factored expression: $\dfrac{10(p {-10}) (p {-9})}{p - 10}$ We can divide the numerator and denominator by $(p + 10)$ on condition that $p \neq 10$ Therefore $x = 10(p - 9); p \neq 10$